NEW YORK -- The notebook on Mario Cuomo's desk is his famous diary. The woman in an adjacent office is Mary Tragale, Cuomo's secretary. Every night, Tragale takes the diary home and types it up. In this respect, she is Cuomo's confessor, privy to his most private thoughts -- the person who should know whether the New York governor is considering a presidential race. Cuomo buzzes Tragale on the intercom to show he is not.

''Mary, is there anything in my diary about running for president?'' Cuomo asks. ''Not very much,'' Tragale's voice responds. ''I don't think you ever thought about running. There's nothing in the diary about it.'' Cuomo smiles, says ''Thank you, Mary'' and switches off the intercom. Cuomo has confirmed he is out of a race he was never really in.

Tragale's testimony is a bit shocking. Almost daily, Cuomo is beseeched to make the Democratic race. On this day alone he's been called by party leaders from all over the country. Gary Hart has just reentered the presidential race. Democrats ask Cuomo to declare his candidacy -- to save the party, to save the nation, maybe even to save their own skins. His answer, as always, is no.

Cuomo writes daily, almost obsessively, in his diary. You would think that there, on paper, he would work things out -- set out the pros, the cons, the one hands and the other hands. You would think that he would note his high standing in the polls, the conventional wisdom that the declared candidates have not caught on, the entreaties from party leaders and, of course, from the wayward journalists who sometimes wander across the line that separates recording events from shaping them.

But the tug of war that was supposed to be playing out in Mario Cuomo's head seems instead to be in the heads of others. Not once, he said, did he ever discuss running for president with his family. Not once did he sit down with his wife, Matilda, and hash things out. On the day he decided to announce he would definitely not be a candidate, he mentioned his intentions to his wife at the door on the way out of the house. The issue was closed.

Why? To Cuomo, the answer is simple: he's not the best man for the job. ''Before a person runs for the presidency, he ought to say that I'm better than anyone else in the field,'' Cuomo said. ''You have to start with an overwhelming conviction in your own superiority.'' Only once, Cuomo said, did he have that feeling -- when he first ran for governor in 1982. He won, he said, because he knew he would be a better governor than his primary opponent, New York Mayor Edward Koch. In other races where he did not feel that confidence, he lost.

When it comes to the presidency, Cuomo has taken his own measure and comes up short. The polls, the clamor, the pleas, the aura of celebrity do not sway him: ''I don't think I'm better. I don't think that when it comes to the presidency.'' He names the declared candidates, their strengths, their experience. He mentions Abraham Lincoln, whose presidency is considered great but who, as a politician, was not highly thought of in his own time. He mentions John Kennedy too -- a mediocre senator, a great president. This could happen to one of the current candidates, Cuomo said. Let the voters make their decision.

Cuomo's modesty is jarring. From his office on the 57th floor of the World Trade Center, you can see all of New York harbor, the Statue of Liberty included. Like any governor, he has his limos and helicopters, his mansion and his state police escorts -- one, in Cuomo's case, that will press his pants for him. (''You know what it's like to hang up your pants and say 'tomorrow'?'') All of this leaves Cuomo unmoved. His instincts tell him that the presidency is not for him.

And yet, Cuomo will not issue a Shermanesque statement that never, under any circumstance, will he run for president -- although he foresees none that would cause him to change his mind. In a previous interview, he asked why he alone should do that. Why not Sen. Bill Bradley (D-N.J.)? Why not Sen. Sam Nunn (D-Ga.)? He says that one of the current Democratic candidates will emerge from the pack and will become a celebrity -- like Cuomo. Then the spotlight will shift and there will be little talk of a Cuomo candidacy. By the 1992 election, Cuomo will be a has-been. ''I'm finished,'' he said.

When I came into Cuomo's office, the governor was on the phone, talking politics and swinging a baseball bat. He's a big man, a former minor-league ballplayer with the solid body of someone who could put it out of the park. Much of the Democratic Party thinks that Cuomo can hit the long ball. Maybe he can, but this year the Democrats are not likely to find out. For reasons of his own, Cuomo won't step up to the plate.